Method of truing gears



1,683.867 lA. W. COPLAND ET AL METHOD oF TRUING GEARS Original FiledApril 10, 1922 6 Sheets-sfiga?. 1

BY M MVL/@ATTORNEY Sept. l1, 1928.

Sept. '11, 1928. 1,683,867

A. W. COPLAND ET AL METHOD OF TRUING GEARS Original Filed April 10. 19226 vSheets-Sheet 2 Bf BY @p/fm ATTORNEY 6 Sheets-Sheet 3 original File'dApri A. W. COPLAND ETT AL METHOD 0F TRUING GEARS Sept. 11, 1928.

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A. W. COPLAND ET AL METHOD OF TRUING GEARS Original Filed April 10, 19226 Sheets-Sheet 4 W INI/'INTORS` JW BY M VMMATTORNEY sept. 11, 192s.1,683,867

A. W. COPLAND Er AL fz E? EEEEEEE fa/Jam? A TTORNE Y INVENToRs sept. 11,192s. 1,683,867

` A. W. COPLAND ET AL A METHOD OF TRUING GEARS Original Filed April 10.1922 6 Sheets-Sheet` 6 ,/H l i! rs Mh! i l1 R7@ 5i S/L! S i INVENTORS'BY am MATTORNEY Patented Sept. 11, 1928.

UNITED STATES PATENT GFF-ICE.

ALEXANDER W. COPLAND, OEBIRMINGHM, MICHIGAN, AND MAXWELL I. MATHEW- soN,OF PROVIDENCE, RHODE ISLAND, AssIGNORs TO DETROIT TRUST COMPANY, OFDETROIT, MICHIGAN, A CORPORATION OE MICHIGAN.

METHOD OF TRUING GEARS. v

HEISSUED Continuation of application Serial No. 551,141, Vfiled April10, 1922, and in Great Britain September 14, 1926 This application iledFebruary 4, 1927. Serial No. 165,867.

The invention relates to a method'of truing toothed gears, or otherbodies having circular series of radiating surfaces, by a grinding orlapping process. Examples of such bodies other than gears are splinedshafts, index plates, etc. Since, however, the truing of toothed gearspresents all aspects of the invent-ion, the latter Will be particularlydescribed ivith reference thereto. The present application constitutes acontinuation of our earlier application Serial No. 551,141, filed Apriiio. i922. n

The objects of the invention comprise the correction of defects, first,with respect to the spacing and alignment of the teeth, second, withrespect to the concentricity of the true pitch circle and the axis ofrotation of the gear, third, with respect to variations orirregularities in the different teeth, and fourth, with respect to thetrue tooth form.

A further object of the invention is to accomplish the foregoing resultsby a simple process susceptible of being carried out by means of simpleapparatus.

The improved method is based upon the principle that the amount ofmaterial removed from a surface being ground is p ropoi-tional first, tothe area of the abrading surface traversing a unit area of the surfaceto be ground, second, thepressure of 'the abrading surface upon a unitarea of the suiface to be ground, and third, the character of theabrading surface. According to this principle, to produce uiiifoi'mgrinding on all portions of a surface contacting ivith the abradingsurface, there must be uniformity in pressure and area. This is not thecase in the ordinary prior processes of lapping gears by rolling thesame With intermesliing gears,

whether the gears are merely revolved or are revolved and also axiallyreciprocated relative to each other. g

According to the present invention there is substituted for theintermeshing spur gear of the piror methods a lap in the form of aninternal gear with teeth complementary .to those of the gear to be truedand having its circular pitch and the diameter of its pitch circleapproximately the same as those of the gear to be trued so as to 'fitover the latter in telescoping relation; With the gear and lap ment asthe relative reciprocation of the-gear and lap proceeds. The relativereciprocatory movement of the gear and lap is intermittently interruptedto permit the gear to be angularly advanced (indexed)A in relation tothe lap so that different teeth Aof the gearV and lap are broughtsuccessively into engagement. In addition the gear and lap are sosupported that limited relative movement of the one in relation totheother in any direction radial to their axes is permitted with the resultthat the torsional pressure referred to causes an automatic centering ofthe gear in relation to the lap. Suitable abrasive is applied to themutuallyl engaging surfaces of the lap and gear.

The lapping effected by carrying out these steps is uniform on allsurfaces which are simultaneously in contact. Furthermore, because ofthe indexing of the gear in relation to the lap irregularties either inindividual tooth form or in the spacing of the teeth are corrected, theeffect of continued laiiping with the progressive change in registrationbeing to continually approach equispacing of the teeth and uniform toothcontour.

lVhile the new method may be carried out with various forms ofapparatus, for the sake of specific illustration and explanation,reference is had to the accompanying drawings showing by Way of examplela form'of apparatus which has been found satisfactory.

Our method may be carried out with various forms of apparatus, but asuitable apparatus is shown in the accompanying drawings, in which Fig.1 is a vertical central section through the machine.

Fig. 1a is a fragmentary vertical section cooperating parts. Fig. 2 is afront elevation, partly in section, Of the machine shown in Fig. 1.

Fig. 3 is an enlarged longitudinal section showing a modified form oflap carrier and through the indexing head on line 3-3 of Fig. 2.

Fig. 4 is a section through said head in the plane of the variabletorque connection on line 4-4 of Fig. 2.

Fig. 5 is a horizontal section substantially on line'- of Fig. 2.

Fig. 6 is a horizontal section on line 6-6 of Fig. 3.

Fig. 7 is a longitudinal section through a construction of annular lapfor modifying the tooth contour.

Fig. 8 is a cross section thereof.

Fig. 9 is a view similar to Fig. 7 of another lap construction forproducing a different modification of the tooth contour.

Fig. 10 is a diagram illustrating the operation of the machine in thecarrying ont of the method.

Figs. 11 and 12 are also diagrams showing the manner of altering thetorque pressure.

As shown in the drawings the apparatus comprises, first, meansfog/"relatively reciprocatin the gear to be ground and its corresponi.1g lapping member, second, means for intermittently progressivelychanging the registration of the teeth of the gear and lap, and third,means for varying the mutual torque pressure of the gear and lap teeth.

Referring in detail to the construction illustrated, A is a suitableframe on which are mounted the center spindles B and C for carrying anarbor D having the gear E to be ound.` F is an annular member carryingthe lap G. This lap, of suitable material such as cast iron, is in theform of an internal gear having the diameter of its pitch circle and itscircular pitch approximately the same as those of the spur gear to beground so as to fit over the latter with the internal teeth of the lapsimultaneously engaging the teeth of the' spur gear. The lap-carryingmember F is arranged concentric to the axis of the spindles B and C andmounted by means of an antifriction bearing N upon a crossheadH whichslides upon ways I on the machine frame. The upper end of the lap isadditionally supported by an antifriction bearing N between the lapanithe c rosshead H. The member F is formed with a depending tubularshank F which slidably engages a fixed bearing Grv carried by themachine frame. The shank F carries splines F which engage straightlongitudinal grooves G in the fixed bearing G. J is a lever forreciprocatin the crosshead H and member F actuated y link K connected toa crank L, said crank being adiustable in throw to vary the length ofthe reciprocation. Obviously the reciprocation of the crosshead Heffects a corresponding reciprocation of the lap G and the spline andgroove connection F G holds the lap against rotational movement. Thusduring each revolution of the crank the lap G will be movedlongitudinally a distance equal to its length plus somewhat more thanthe width of the gear to be ground, thereby passing into and out ofengagement with the gear at opposite ends of each stroke. As the fixedspindle B is long and slender and supported only at its lower end it ispermit-- ted to flex slightly and thus its upper end forms a support forthe gear and arbor adapted to move laterally somewhat in any directionrelative to the lap and its support.

To change the registration of the gear and the lap on successivestrokes, an intermittently operating indexing mechanism is provided.This comprises a dog O on the arbor D, which is engaged by pins or lugsO on a rotatablemember- O2 secured, as by screws, to ratchet wheel Rwhich in turn is keyed to a sleeve O3. The keyed connection between theratchet R and the sleeve O3 is made secure by the Spanner nut O4 whichis threaded un the sleeve O3- The latter member is mounted with a lostmotion connection on the extended hub P' of the gear Q, the lost motionconnection being formed by the lug P on the hub P engaging a slottedbearing in the member O3 (see Fig. 6). A light coil spring P2 in theslotted bearing serves -to hold the lug normally in driving contact withthe member O3. A nut P3 on the end of sleeve C2 engages hub P and sleeveO3 to hold them rotatably on sleeve C2. The gear Q is connected by agear train with the drive mechanism for the crank L, said trainincluding a Geneva stop movement, or equivalent device, for convertingthe continuous rotary motion of the drive into intermittent rotation ofthe member D. This, in detail, comprises a gear wheel Q on a shaft Q2connected by the Geneva stop movement Q3 with a shaft Q4, which latteris connected by a flexible shaft Q5 with the shaft Q6 driven by bevelgear wheel Q7 from the crank shaft. The arrangement is such that twiceduring each revolution of the crank shaft, rotary motion is transmittedto the member O suficient to advance the teeth of the gear wheel beingground into registration with other interdental spaces of the lap. Thismovement is effected during the portions of the cycle of the crank wherethe gear wheel is out of engagement with the lap, so that in successivereciprocations or strokes of the craik the gear wheel has differentangular engagements with the lap.

As has been stated,.the pressure of the lap against the gear wheel perunit area. is.one factor determining the grinding action. Where the lapis moved into and out of engagement with the gear wheel it is evident Athat during initial engagement the area of contact is small and isrogressively increased until the whole of t e gear is in contact withthe lap. Therefore, if the torque Y turn is actuated by a rod R4.

pressure on the arbor D were to remain uniform, there would be a greatergrinding action at the ends of the stroke where the contact area isvlimited than at the center of the stroke wherethefull area is inengagement. Such a result is avoided by varying the torque pressureduring engagement and disengagement and with the construction shown thisis accomplished by transmitting the torque through a spring and suitablyvarying the tension of the spring, the specific devices employed beingas follows:

The ratchet wheel R which is exchangeably mounted on member C3 andcarries the member 02, is engaged by a pawl R carried by a slide R2mounted in the frame. This slide is yieldably actuated by a spring R3,which in S is a member mounted on the crossshead H which is providedwith a cam portion S for engaging the rod R4 and actuating the same toplace a tension on the spring R3. The parts are so constructed andarranged that when the gear wheel is out of engagement with the lap, nopressure will be exerted by the cam on the rod R4, and consequently thespring R3 will be at zero tension. 0n the other hand, when the gearwheel enters engagement with the lap, the cam S also engages the rod R4progressively moving the latter and thereby increasing the tension ofthe spring R3. The movement imparted to the rod R4 is completed as thegear becomes fully engaged with the lap so that intermediate the pointof initial engagement and the point of full engagement the tension ofthe spring R3 has been increased from zero to a predetermined maximumamount. The tension then remains constant during the further relativereciprocating movement of the lap in relation to the gear until at theopposite end of its stroke it again passes out of engagement, at whichtime the cam S gradually relieves the tension of the spring tocorrespond to the diminishing area. of contact. This variation intension is permitted by the lost-motion connection between the member O3and the member P formed by the lug P' engaging the slotted bearing. Thusthe pressure of the lap against the gear wheel will be'maintainedsubstantally constant per unit area of surface engagement. Tt is to beobserved in this connection that if the pressure is to be kept constant,as last referred to, the speed of the machine should not be too greatelse the application of the pressure by the cam V through the spring U,especially in the case of narrow gears, will betoo sudden and notcontrolled in accordance with the shape of the cam. i

lt will be noted on reference to Figs. 2, 4 and 5 that a duplicate setof pawl carrying and actuating parts R2, R3 and R4 are provided at thediametrically opposite side of ratchet wheel R and that a second cam Sis provided to actuate them. Thus by changing the pawl R from onecarrier R2 to the other and turning over the ratchet wheel R, it ispossible to lapboth sides of the teeth of a gear without turning thelatter over.

To facilitate engagement and disengagement of the work the centerbearing C, together with the sleeve C2, can be raised and lowered by thelever C', having the clamp C3. This permits of withdrawing the centerwhenever the work arbor D is to be disengaged for the removal offinished work and the engagement of new work to be ground. v

In carrying out the improved method of the present invention by theapparatus just described, or any other suitable means, one proceeds asfollows: The gear wheel, or other object to be ground, is mounted eithersingly or in series on the arbor D and the latter is engaged with thecenter spindles B and C. A corresponding lap G is attached to theannular member F and arranged in registration with the gear wheel. Thesurface of the lap is then coated with abrasive material, afterwhichrmotion is imparted to the machine to cause a reciprocation of thelap relative to the gear. At the same time the torque pressure on thegear is varied as above described, so that during contact with thelatter there will be` a uniform pressure per unit of contact area. Aftereach reciprocation or strokey the indexing mechanism advances the gearinto a different position of registration so that the contactingsurfaces are changed after each stroke. The lapping thus effected iscontinued Auntil the desired truing of the gear is effected.

Assuming that in the gear to be ground one or more of the teeth aredistorted so as to come into contact with the lap in advance of theothers, these advanced surfaces will first be ground away as will alsothe contacting portions of the lap. However, by reason of theprogressive change in registration, the wearing away of the lap isuniformly distributed over a number` or all of the teeth thereof,whereas the grinding upon the gear continues on the high spots untilthese are reduced to the level of the other portions. Assuming againthat the lap is inaccurate, having certain portions of its surface inadvance of the true form. these advanced portions will therefore firstcome in contact with the gear teeth and will be progressively groundaway. There will alsobe av grinding action upon the gear teeth, but dueto the progressive change in registration. this grinding is not all on.any one tooth but is distributed over a plurality of teeth. Therefore,not only the gear but also the lap will constantly approach the trueform as the grinding proceeds. In other words, the effect of continuedfirst released.

grinding is to average the contour and circular pitch of all of theteeth in both the gear and the lap and if this average is the true form,the gear will be rendered true. Since 5 the supporting-spindle B iscapable of moving laterally somewhat at its upper end, the gear has in ameasure a floating support. Hence when mutital torsional pressure isexerted between three or more circumferentially 13 spaced teeth of thelap and a corresponding number of the gear teeth, the gear moveslaterally in a manner tending to center itself ,relative to the lap or,in other words, in a manner tending to bring the pitch circles of thegear and lap into coincidence. This centering `action continues as longas the mutual torsional pressure is exerted and the result is that allthe teeth of the gear are lapped to approximately their true contourwith respect to a common gear axis and corresponding pitch circle withthe removal of a minimum amount of material from the tooth surfaces.

In case the average tooth formsecured by the above procedure is notthetrue or desired form, duc either to the original cutting or to anyother cause. the process as thus far described is incapable of producingthe true form We may, however, by a modification of the method correctan inaccurate average form b v employing a modified vlap construction.This modified methd forms the subject matter of ouil application forpatent,

Serial No. 551,140, filed April 10, 1922. In

brief it consists in differentially interrupting the surface of the lapso as to produce a greater grinding effect on one portion of the geartooth than on another. For instance, if the crown portion of the geartooth projects beyond 'thetrue involute curve desired, this portion maybc ground to a greater extent than the root portion by cutting notches Win the teeth of the lap. as shown in Fig. 7. Thus the amount of surfacein the lap whichrubs over the root of the gear tooth is less than theamount of surface rubbing over the crown portion of said tooth whichresults in removing more material from the crown lportion and moreclosely approximating the true involute curve. The revers effect may beproduced by using a lap such as shown in Fig. 9, with teeth cut awaymore at the root .than at the. crown, as indicated vat W', the effect ofthis being to grind more at the root ofthe gear tooth than at the crownthereof.

The invention is also applicable 'to the grinding of helical gears, themodification of the apparatus shown in Fig. 1 being applicable for thispurpose. Here the fixed bear-l ing G has helical grooves G2 instead ofthe straight grooves G offthe first construction. The construction istherefore such that during` thereciprocation of the holder F the lapwill be t-urned by the mutual engagement ,ofcf

the splines F and the helical. grooves G2,

. torsional pressure is applied through the gear,

it is obvious that the result will be the same whether these respectiverelative movements and torsional pressure of the lap and gear areeffected entirely through one or the other of said members or in partthrough one of them and in part through the other.

While the improved method has been Adescribed as applied to the grindingof gears, as has previouslybeen pointed out, it is applicable to thegrinding of other bodies having radiating surfaces arranged in uniformcircular series. By uniform circular series we 85 mean one in which theradiating surfaces are so spaced that the circumferential or circularApitch dista-nce between any two of said surfaces is either equal to ora multiple of the circular pitch distance between adjacent radiatingsurfaces.

Also, it is obvious that our process is equally applicable to thegrinding of both internal and external gears or other bodies. Thus ifthe gear or body to be ground has its teeth, or parts with radiatingsurfaces, on an external perimeter, the lap will have its complementary,oppositely toothed or surfaced parts on an internal perimeter thereof;and, vice versa, if the gear or other body to be 193 ground( hasinternal teeth or radiating surfaces, the lap will have external teethor radiating surfaces. In all cases the pitch circles of the gear andlap will be approximately equal in diameter, and in all cases the teethof the lap, or its parts with radiating surfaces, will have contoursparallel to the tooth contours of the gear or body to be lapped. Vecmplo the expressions oppositel toothed?, oppositely surfaced toindicate the complementary internal-external arrangementl of the teethor radiating surfaces ofthe gear and lap, respectively, or of the lapand gear, respectively, as the case may be. While it is preferable onaccount of greater ease of .manufacture to make thelap teeth fullycomplementary to the teeth of the gear or the like to be trued, it willbe understood that the only complementary relation between the lap andgear teeth which is necessary is that between the active lappingsurfaces, and, since only one side of a tooth can be active atone time,it would be possible to lap a gear by our method with a lap having teethwith I the/complementary formation on one side only, it being. onlynecessary after lapping one side of the gear teeth to turn the gear overin order to lap the other sides of its teetl1. Also, the term pitchcircle when apoppositely disposed teeth and -110 I plied to toothedgears, -is to be understood in its usual technical sense applicable tosuch gears, whereas when applied to other bodies having radiatingsurfaces in circular series it is to be understood as the circle definedby the mean radius of the radiating surfaces.

In our method the effect of continued use of a lap is to true the samein the same Way that the gear is tru'ed, and consequently initialinaccuracies in the lap are in a measure corrected by use thei'eof. Thisaspect of our invention is of greater importance where equi-spacing ofthe teeth of the gear is the thing chiefly sought, since equi-spacing ofthe lap teeth is very thoroughly effected by continued use of the lap.If a particular form of gear tooth is to be strictly adhered to weprefer to correspondingly form the lap teeth as accurately as may beinitially. Also, it is to be observed that While the use of modified orcorrective laps renders high accuracy in the original cutting of t-hegear unnecessary since the desired modification of the gear tooth can beeffected by the lap, it is obviously desirable if possible to cut thegears with sufficient accuracy so that the use of the modified lap isnot required.

lWhile the foregoing detailed description sets forth the preferred.procedure it will be understood that the procedure described can bevaried without departing from the invention as defined in the appendedclaims.

What We claim is:

1. The method of grinding gears comprising registering the gear to beground and a lap having a parallel tooth contour, axially reciprocatingthe one with respect to the other into and out of mutual engagement,maintaining substantially throughout the mutual overlapping relation ofthe tWo substantially uniform torque pressure per unit area of mutualengagement, and progressively changing the registration between theteeth of the lap and those of the gear.

2. The method ofgrinding gears which comprises registering the gear tobe ground and a lap having a parallel tooth contour, axiallyreciprocating one with respect to the other, progressively rotativelyadvancing one with respect to the other while out of engagement tochange the registration of the teeth, maintaining between the gear andlap substantially uniform torque pressure during said reciprocationwhile said gear and lap are in full Contact, and Varying the torque"pressure while the said gear and lap are entering upon and passing outof full contact to maintain substantially equal pressure per unit aieaof contact. i

3. The method of grinding gears whichmutual engagement, progressivelyrotatively advancing one with relation to the other While they are outof mutual engagement to change the registration of the teeth, andmaintaining throughout the mutually overlapping relation ofthe two atorque pressure of the one on the other which is substantially constantper unit area of mutual engagement.

4. The method of grinding gears which comprises registering the gear tobe ground and a lap, said parts being in the relation of axiallycoincident intermeshing internal and external gears, axiallyreciprocating one with respect to the other, rotatively advancing one inrelation to the other after each reciprocation to change theregistration of the teeth, maintaining a substantially uniform torquepressure of the one against the other while said parts are in fullengagement, and varying the torque pressure at the entering upon andpassing out of full engagement to maintain substantially uniformpressure per unit area of engagement.

5. The method of grinding a body, such for example as a toothed gear,having at its perimeter radiating surfaces arranged in auniform'circular series, said method comprising registering the bodywith a complementary oppositely surfaced lap having its radiatingsurfaces parallel in contour to those of said body and disposed in apitch circle of approximately the same diameter as that of 4said' body;axially reciprocating one in telescoping relation to the other;maintaining atorsional pressure of one upon the other during saidreciprocation; and progressively changing the registration of the bodyand lap by intermittently angularly advancing one in relation to theother while they are out of mutual engagement.

6. The method of grinding a body, such for example as a toothed gear,having at its perimeter radiating surfaces arranged in a unifoi'incircular series, said method comprising coaxially registering the bodywith a lap having a lurality of radiating surfaces oppositely isposedand of parallel contour to the radiating surfaces of the body, the saidlap having its radiating surfaces spaced around a.- pitch circle ofapproximately the same diameter as the pitch circle of the said body andat distances from each other which are equal to or multiples of thecircular pitch `of the radiating surfaces of said body; axialving theirreciprocational engagement; and

progressively changing the registration of the body and lap byintermittently angularly advancing one in relation to the other Whilethey are out of mutual engagement.

7. The method of Agrinding toothed gears which comprises coaxiallyregistering the gear to be ground with a lap having oppositely disposedteeth of parallel contour and approximately the same circular pitch asthe gear; axially reciprocating one in telescoping relation totheiother; maintaining a torsional pressure of one upon the other duringsaid reciprocation; and progressively changing the registration of thegear and lap by intermittently angularly advancing one in relation tothe other while they are out of mutual engagement.

S. The method of grinding gears which comprises registering a gear to beground and a lap in the relation of axially coincident internal andexternal intermeshing gears, in axially reciprocating the one Withrespect to the other in mutual abrasive contact, and in intermittentlyprogressively rotatively advancing the one in relation to the other tochange the registration of the teeth. i 9. The method of accuratelyequi-spacing a circular series of surface portions of like contour of abody, such for example as a toothed gear, Which comprises coaxiallyregistering the same With a lap having a circular series ofcomplementary oppositely surfaced portions, axially reciprocating'theone With respect to the other in mutual abrasive contact, andprogressively angularly changing the registration of the body and lap.

10. The method of accurately equi-spacing a circular series of radiatingsurfaces of a body, such for example as a toothed gear, which consistsin coaxially registering the same with a lap having a plurality ofsurfaces oppositely disposed and of parallel contour to said surfaces ofthe body, the said surfaces of the lap being spaced around a pitchcircle of approximately the same diameter as the pitch circle of thebody and at distances from each other Which are equal to or multiples ofthe circular pitch of the body; axially reciprocating the one Withrespect to the other in mutual abrasive contact; and progressivelyangularly changingthe registration of the body and lap.

11. The method of grinding a body, such for example as a. toothed gear,having at its perimeter radiating surfaces arranged in a uniformcircular series, said method comprising coaxially registering the bodyWith a complementary oppositely surfaced lap having its radiatingsurfaces parallel in contour to those of said body' and disposed in apitch circle of approximately the same diameter as that of said body;creating a mutual torsional pressure between the radiating surfaces ofthe body and lap and thereby moving their pitch circles intocoincidence; axially reciprocating one in telescoping relation to theother while maintaining said torsional pressure; and progressivelychanging the registration of the body and lap by intermittentlyangularly :advancing one in relation to the other While they are out ofmutual engagement.

12. The method of grinding a body, such for example as a toothed gear,having at its perimeter radiating surfaces arranged 1n a uniformcircular series, said method comprising coaxially registering the bodyWith a lap having a plurality of radiating surfaces oppositely disposedand ofyparallel contour to the said surfaces of the body, the radiatingsurfaces of the lap being spaced around a 'pitch circle of approximatelythe same diameter as the pitch circle of the body and at distances fromeach other Which are equal to or multiples of the circular pitch of thebody; creating a mutual torsional pressure between the radiatingsurfaces of the body and the lap and thereby'moving their pitch circlesinto coincidence; axially reciprocating one in Vtelescoping relation tothe other While maintaining said torsional pressure; and progressivelychanging the registration of the body and lap by intermittentlyangularly advancing one in relation to the other While they are out ofmutual engagement.

13. The method of grinding helical toothed gears which comprisescoaxially registering the gear to be ground Wit-h a lap havingoppositely disposed teeth of parallel contour and approximately the samecircular pitch as the gear; causing a combined axial and rotationalmovement of the one member relative to the other; maintaining atorsional pressure of one upon the other during said relative movement;and progressively changing the registration of the gear and lap byintermittently angularly advancing one in relation to the other Whilethey are out of mutual engagement.

14. The method of grinding helical toothed gears Which comprisescoaxially registering the gear to be ground with alap having oppositelydisposed teeth of parallel contour and approximately the same circularpitch .as the gear; causing a combined axial and rotational Imovement ofthe one member relative to the other, Iwhich movement is positivelydetermined independently of said other member; maintaining a torsionalpressure of one upon the other during said relative movement; andprogressively changing the registration of the gear and lap byintermittently angularly advancing one in relation to the other Whilethey are out of mutual engagement.

15. A method of lfinishing gear Wheels according to which an internalgear Wheel is disposed completely to encircle an external gear Wheel,the teeth of said gear Wheels being equal in 'number and complementaryin shape, and said gear Wheels by relative axial reciprocating motionare then subjected to a series of mutual grinding actions withintermediate circumferential adjustments to engage successively'different teeth of said gear Wheels, as set forth.

16. A method of finishing gear Wheels shape, torque is applied to bringcorresponding tooth faces of said gear Wheels into operat1ve contact,and sa1d gear Wheels by relative axial reciprocatmg motion are thensub.-

jected to a series of mutual grinding actions with intermediatecircumferential adjust- 10 ments to engage successively different teethot' said gear wheels, as set forth.

In testimony whereof, We hereunto ax our signatures.

ALEXANDER W. COPLAND. MAXWELL I. MATHEWSON.

